$D$-glucose and $D$-fructose can be differentiated by

Suppose that the points $(h, k)$,$(1, 2)$,and $(-3, 4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h, k)$ and $(4, 3)$ is perpendicular to $L_1$,then $\frac{k}{h}$ equals

The radius of the smallest electron orbit in a hydrogen-like ion is $(0.51 \times 10^{-10} / 4) \text{ m}$. This ion is:

In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

$\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x=$

If $\frac{x}{(x - 1)(x^2 + 1)^2} = \frac{1}{4}\left[ \frac{1}{(x - 1)} - \frac{x + 1}{x^2 + 1} \right] + y$,then $y =$